I've noticed that when I'm out at night stars seem to vanish when I focus on them. I assume the reason is physiological and not astronomic. Why does this happen? I would expect that things would be more clear when I focus on them.

You might also notice this phenomenon while lying in bed, e.g. the dim glow from the illumination of a digital clock or small LED is often visible only if you look away (using peripheral vision).
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Mechanical snailSep 16 '12 at 4:38